How to notice duplicate geometry?
Usually doubles and duplicate geometry are unintentional, but sometimes you might have geometry that is intentionally in close proximity to other geometry so that you can't just do a remove doubles on the entire object.

There's a couple of Low-Tech ways that i'd like to suggest first.


If you press Z, in edit mode, you'll see a transparent / half opaque mesh. Faces that are duplicated in place will often appear darker. 
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Keep in mind that Backfacing Faces will also appear darker, so don't get confused :) 
In Object mode, you'll see duplicate edges because they are drawn using the same color as the border of a mesh. Whether or not this is intentional I don't know, but it works well to track down duplicates edges.

In Face selection mode of Edit Mode, look for Dots on edges. Dots indicate the median of a face and should never been visible on edges.

You see this with geometry that you've accidentally extruded without translating the new face.
In vertex selection mode of Edit Mode, look for vertices which don't highlight surrounding edges: